Modified Principal Component Analysis: An Integration of Multiple Similarity Subspace Models

Abstract

We modify the conventional principal component analysis (PCA) and propose a novel subspace learning framework, modified PCA (MPCA), using multiple similarity measurements. MPCA computes three similarity matrices exploiting the similarity measurements: 1) mutual information; 2) angle information; and 3) Gaussian kernel similarity. We employ the eigenvectors of similarity matrices to produce new subspaces, referred to as similarity subspaces. A new integrated similarity subspace is then generated using a novel feature selection approach. This approach needs to construct a kind of vector set, termed weak machine cell (WMC), which contains an appropriate number of the eigenvectors spanning the similarity subspaces. Combining the wrapper method and the forward selection scheme, MPCA selects a WMC at a time that has a powerful discriminative capability to classify samples. MPCA is very suitable for the application scenarios in which the number of the training samples is less than the data dimensionality. MPCA outperforms the other state-of-the-art PCA-based methods in terms of both classification accuracy and clustering result. In addition, MPCA can be applied to face image reconstruction. MPCA can use other types of similarity measurements. Extensive experiments on many popular real-world data sets, such as face databases, show that MPCA achieves desirable classification results, as well as has a powerful capability to represent data.

Research on multi-effect evaporation salt prediction based on feature extraction

“…Experiments show that this algorithm can better extract useful features in the data set. By improving the PCA algorithm, Fan et al proposed a learning framework based on multiple similarity metric subspaces, namely an improved principal component analysis (MPCA) algorithm 22 . MPCA calculates three similarity matrices according to the similarity measurement method: interactive information matrix, angle information matrix, and Gaussian kernel similarity matrix.…”

RMSC: Robust modeling of subspace clustering for high dimensional data

“…Geometric [22] Sensitive to noise and Outlier into the data Complexity is exponential to the number of subspace dimension. Statistical Principal Component Analysis [23] The number and dimensions of the subspaces should be known Multistage learning [24] [25] Sensitive to initialization. Robust Statistical Approach [26] Dimension of subspace need to be known and equal agglomerative lossy compression [27] Complexity is exponential to the number of subspace dimension There is No Theoretical proof for the optimality of the agglomerative algorithm.…”

Mainlobe interference cancellation based on PCA + ECA in passive bistatic radar

“…The mainlobe interference with the high power can be treated as the principal component of the echo. So the principal component analysis (PCA) algorithm can be exploited to extract the mainlobe interference [6, 7]. The complete signal processing structure of the proposed method is showed in Fig.…”